Question

A wire of length 240 inches is cut into 2 equals pieces. Each piece of wire is then bent into forming an equilateral triangle and a square. Determine the sum of the areas of both figures.

Answer 1

240 inches cut into 2 equal pieces is just taking half of the wire.
Making the two pieces of wire 120 inches.
If you bend one 120 inch wire into a square, that means that each side equals 30 inches. (A square has 4 sides. 120/4 = 30)
An area of a square is length times width, which the length equals 30 and width equal to thirty. 30 * 30 = 900. square inches.
120 wire bent into a triangle makes each side equal to 40. 120/3=40. The area of an equilateral triangle is height times width. The width is just one of the sides (40 inches) but the height needs some geometry. To find the height you need to use either 30 times sin(60) or 30 times cos(30), both are equal. To be clear, I will leave the height as 30sin(60). The area will be equal to
`40*30sin(60)`
which can be simply written as 1200sin(60).
So the sum of both areas is
`(1200sin(60)+900)`